6.1. Creep Modeling Approaches

Several mathematical models are used to predict the long-term creep behavior of concrete. These are especially important in structural design software and finite element analysis.

This introductory statement sets the stage for discussing different mathematical models that engineers use to predict how concrete will deform over time under a constant load. The significance of these models lies in their application in structural design and analyses, which helps ensure that buildings and structures remain safe and functional throughout their lifespan.

Think of these mathematical models as weather forecasts for concrete. Just as meteorologists predict climate behavior based on various atmospheric factors, engineers use these mathematical tools to foresee how concrete will behave under different loads over time.

a) Linear Viscoelastic Model

• Assumes that concrete behaves like a combination of springs (elastic elements) and dashpots (viscous elements).
• Common analogs:
  • Maxwell Model (series combination of spring and dashpot)
  • Kelvin-Voigt Model (parallel combination)
  • Burger's Model (Maxwell + Kelvin-Voigt)

The Linear Viscoelastic Model treats concrete as a mix of springs and dashpots. Springs represent the elastic response (immediate deformation), while dashpots illustrate viscosity (time-dependent deformation). The three common analogs explain different ways to conceptualize this model:

1. Maxwell Model: Combines a spring and a dashpot in series, meaning that the total deformation depends on the immediate elastic deformation of the spring and the slow deformation of the dashpot.
2. Kelvin-Voigt Model: Combines them in parallel, where the spring's immediate elastic response and the dashpot's time-dependent response happen together but affect the total strain differently.
3. Burger's Model: Combines both concepts, offering a comprehensive description of how concrete deform under both immediate and long-term conditions.

Imagine a sponge when it's soaked with water. If you press down on it, it compresses quickly (like a spring) and then slowly leaks water (like a dashpot) over time. The Linear Viscoelastic Model helps predict how this 'sponge' (concrete) will behave under sustained pressure.

b) Creep Compliance Function (J(t, t₀)) ε(t)=J(t,t₀)⋅σ Where:

• ε(t): total strain at time t
• σ: applied constant stress
• J(t,t₀): compliance function, depending on loading time t₀

The Creep Compliance Function is a mathematical relationship that helps calculate the total strain (deformation) in concrete at any given time t. It relies on the applied constant stress and a compliance function J(t, t₀) that varies based on when the load was applied (t₀). This function effectively reflects how quickly and how much the concrete will deform over time, emphasizing the time-dependent nature of creep.

Consider placing a heavy backpack on a soft chair. Initially, the chair might resist the weight (like the elastic strain), but over time, it starts to sag (creep) permanently. The Creep Compliance Function helps to quantify that sagging based on how heavy the backpack is and how long it's been weighing down the chair.

c) Creep Coefficient Method (φ(t, t₀)) Creep strain ϕ(t,t₀)= Instantaneous elastic strain at t₀

The Creep Coefficient Method provides a way to express creep strain as a ratio to the instantaneous elastic strain when the load is first applied. This method is widely used in design standards, offering a practical means for engineers to account for creep behavior in their calculations. The φ(t, t₀) shows how much additional strain can be expected as time progresses, framed as a function of the initial load application time.

Imagine filling a balloon with air. When you first blow it up (apply load), it expands immediately (instantaneous elastic strain). Over time, as the balloon continues to stretch, it loses some air and sags a bit more (creep strain). The Creep Coefficient Method helps predict how much more it will sag in the future compared to its initial expansion.

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